theorem :: FDIFF_11:54

for Z being open Subset of REAL st Z c= ].(- 1),1.[ holds
( (arctan - arccot) / exp_R is_differentiable_on Z & ( for x being Real st x in Z holds
(((arctan - arccot) / exp_R) `| Z) . x = (((2 / (1 + (x ^2))) - (arctan . x)) + (arccot . x)) / (exp_R . x) ) )